共查询到20条相似文献,搜索用时 31 毫秒
1.
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and discuss some applications to the study of deformations of regular Hom-Lie conformal algebras. Also, we introduce α~k-derivations of multiplicative Hom-Lie conformal algebras and study their properties. 相似文献
2.
In this paper, we study extensions between two finite irreducible conformal modules over the Schrödinger–Virasoro conformal algebra and the extended Schrödinger–Virasoro conformal algebra. Also, we classify all finite nontrivial irreducible conformal modules over the extended Schrödinger–Virasoro conformal algebra. As a byproduct, we obtain a classification of extensions of Heisenberg–Virasoro conformal modules. 相似文献
3.
设f:M^m→R1^m+1是无脐点类空超曲面,则在Mm上可以定义四个基本的共形不变量:共形度量g,共形1-形式C,共形第二基本形式B,共形Blaschke张量A.如果存在光滑函数λ和常数μ,使得A+μB=Ag,则称M^m是拟迷向类空超曲面.本文不仅构造了拟迷向类空超曲面的例子,同时在相差R1^m+1的一个共形变换下,本文还完全分类了拟迷向类空超曲面. 相似文献
4.
Bayram Ṣahin 《Acta Appl Math》2010,109(3):829-847
Riemannian maps were introduced by Fischer (Contemp. Math. 132:331–366, 1992) as a generalization isometric immersions and Riemannian submersions. He showed that such maps could be used to solve the
generalized eikonal equation and to build a quantum model. On the other hand, horizontally conformal maps were defined by
Fuglede (Ann. Inst. Fourier (Grenoble) 28:107–144, 1978) and Ishihara (J. Math. Kyoto Univ. 19:215–229, 1979) and these maps are useful for characterization of harmonic morphisms. Horizontally conformal maps (conformal maps) have
their applications in medical imaging (brain imaging)and computer graphics. In this paper, as a generalization of Riemannian
maps and horizontally conformal submersions, we introduce conformal Riemannian maps, present examples and characterizations.
We show that an application of conformal Riemannian maps can be made in weakening the horizontal conformal version of Hermann’s
theorem obtained by Okrut (Math. Notes 66(1):94–104, 1999). We also give a geometric characterization of harmonic conformal Riemannian maps and obtain decomposition theorems by using
the existence of conformal Riemannian maps. 相似文献
5.
M. Roitman 《Selecta Mathematica, New Series》2000,6(3):319-345
The main objective of this paper is to study embeddings of Lie conformal algebras into associative conformal algebras. We prove that not all Lie conformal algebras admit such embeddings. However, in many important cases, including semisimple Lie conformal algebras of finite type, embeddings of this form exist and sometimes we can even describe universal enveloping associative conformal algebras of Lie conformal algebras and prove an analogue of the classical Poincaré-Birkhoff-Witt theorem. 相似文献
6.
In this article, we prove that various classical conformal diffeomorphism groups, which are known to be essential (Banyaga,
J Geom 68(1–2):10–15, 2000), are in fact properly essential. This is a consequence of a local criterion on a conformal diffeomorphism in the form of
a cohomological equation. Furthermore, we study the orbit of a tensor field under the action of the conformal diffeomorphism
group for these classical conformal structures. On every closed contact manifold, we find conformal contact forms that are
not diffeomorphic. 相似文献
7.
在文[Classification of type I time-like Hyperspaces with parallel conformal second fundamental forms in the conformal space,Acta Mathematica Sinica,Chinese Series,2011,54(1):125-136]中,我们已对共形空间中具有平行的共形第二基本形式的I型类时超曲面作了分类,本文将探讨其他类型的类时超曲面并完全分类共形空间中具有平行的共形第二基本形式的类时超曲面. 相似文献
8.
9.
A vector field on Riemannian manifold is called conformal Killing if it generates oneparameter group of conformal transformation. The class of conformal Killing symmetric tensor fields of
an arbitrary rank is a natural generalization of the class of conformal Killing vector fields, and appears in different geometric
and physical problems. In this paper, we prove that a trace-free conformal Killing tensor field is identically zero if it
vanishes on some hypersurface. This statement is a basis of the theorem on decomposition of a symmetric tensor field on a
compact manifold with boundary to a sum of three fields of special types. We also establish triviality of the space of trace-free
conformal Killing tensor fields on some closed manifolds. 相似文献
10.
In this paper, we study conformal transformations in complex Finsler geometry. We first prove that two weakly Kähler Finsler metrics cannot be conformal. Moreover, we give a necessary and sufficient condition for a strongly pseudoconvex complex Finsler metric to be locally conformal weakly Kähler Finsler. Finally, we discuss conformal transformations of a strongly pseudoconvex complex Finsler metric, which preserve the geodesics, holomorphic S curvatures and mean Landsberg tensors.
相似文献11.
Ye-Lin Ou 《Annals of Global Analysis and Geometry》2009,36(2):133-142
This paper studies conformal biharmonic immersions. We first study the transformations of Jacobi operator and the bitension
field under conformal change of metrics. We then obtain an invariant equation for a conformal biharmonic immersion of a surface
into Euclidean 3-space. As applications, we construct a two-parameter family of non-minimal conformal biharmonic immersions
of cylinder into and some examples of conformal biharmonic immersions of four-dimensional Euclidean space into sphere and hyperbolic space,
thus providing many simple examples of proper biharmonic maps with rich geometric meanings. These suggest that there are abundant
proper biharmonic maps in the family of conformal immersions. We also explore the relationship between biharmonicity and holomorphicity
of conformal immersions of surfaces.
相似文献
12.
13.
We construct a conformally invariant vector bundle connection such that its equation of parallel transport is a first order system that gives a prolongation of the conformal Killing equation on differential forms. Parallel sections of this connection are related bijectively to solutions of the conformal Killing equation. We construct other conformally invariant connections, also giving prolongations of the conformal Killing equation, that bijectively relate solutions of the conformal Killing equation on k-forms to a twisting of the conformal Killing equation on (k−?)-forms for various integers ?. These tools are used to develop a helicity raising and lowering construction in the general setting and on conformally Einstein manifolds. 相似文献
14.
We discuss the conformal boundary of a warped product of two length spaces and provide a method to calculate this in terms
of the individual conformal boundaries. This technique is then applied to produce CAT(0)-spaces with complicated conformal
boundaries. Finally, we prove that the conformal boundary of an Hadamard n-manifold is always simply connected for n≥3, thus providing a bound for the level of complication of the boundary of such a manifold.
相似文献
15.
We define a family of probability measures on the set of Riemannian metrics lying in a fixed conformal class, induced by Gaussian probability measures on the (logarithms of) conformal factors. We control the smoothness of the resulting metric by adjusting the decay rate of the variance of the random Fourier coefficients of the conformal factor. On a compact surface, we evaluate the probability of the set of metrics with non-vanishing Gauss curvature, lying in a fixed conformal class. On higher-dimensional manifolds, we estimate the probability of the set of metrics with non-vanishing scalar curvature (or Q-curvature), lying in a fixed conformal class. 相似文献
16.
Wei Wang 《Journal of Mathematical Analysis and Applications》2008,345(2):777-782
We prove the Korn's inequality for the conformal Killing operator on pseudo-Euclidean space Rp,q, and an existence theorem for solutions to the non-homogeneous conformal Killing equation, which is a pseudo-Euclidean conformal generalization of Donati's theorem for Euclidean Killing operator. 相似文献
17.
We introduce the formalism of differential conformal superalgebras, which we show leads to the “correct” automorphism group functor and accompanying descent theory in the conformal setting. As an application, we classify forms of N=2 and N=4 conformal superalgebras by means of Galois cohomology. 相似文献
18.
Olivier Biquard 《Inventiones Mathematicae》2002,148(3):545-607
A conformal metric on a 4-ball induces on the boundary 3-sphere a conformal metric and a trace-free second fundamental form.
Conversely, such a data on the 3-sphere is the boundary of a unique selfdual conformal metric, defined in a neighborhood of
the sphere. In this paper we characterize the conformal metrics and trace-free second fundamental forms on the 3-sphere (close
to the standard round metric) which are boundaries of selfdual conformal metrics on the whole 4-ball. When the data on the
boundary is reduced to a conformal metric (the trace-free part of the second fundamental form vanishes), one may hope to find
in the conformal class of the filling metric an Einstein metric, with a pole of order 2 on the boundary. We determine which
conformal metrics on the 3-sphere are boundaries of such selfdual Einstein metrics on the 4-ball. In particular, this implies
the Positive Frequency Conjecture of LeBrun. The proof uses twistor theory, which enables to translate the problem in terms
of complex analysis; this leads us to prove a criterion for certain integrable CR structures of signature (1,1) to be fillable
by a complex domain. Finally, we solve an analogous, higher dimensional problem: selfdual Einstein metrics are replaced by
quaternionic-K?hler metrics, and conformal structures on the boundary by quaternionic contact structures (previously introduced
by the author); in contrast with the 4-dimensional case, we prove that any small deformation of the standard quaternionic
contact structure on the (4m−1)-sphere is the boundary of a quaternionic-K?hler metric on the (4m)-ball.
Oblatum 29-XI-2000 & 7-XI-2001?Published online: 1 February 2002 相似文献
19.
S. Deshmukh 《Annali dell'Universita di Ferrara》2011,57(1):17-26
It is known that a conformal vector field on a compact Kaehler manifold is a Killing vector field. In this paper, we are interested
in finding conditions under which a conformal vector field on a non-compact Kaehler manifold is Killing. First we prove that
a harmonic analytic conformal vector field on a 2n-dimensional Kaehler manifold (n ≠ 2) of constant nonzero scalar curvature is Killing. It is also shown that on a 2n-dimensional Kaehler Einstein manifold (n > 1) an analytic conformal vector field is either Killing or else the Kaehler manifold is Ricci flat. In particular, it follows
that on non-flat Kaehler Einstein manifolds of dimension greater than two, analytic conformal vector fields are Killing. 相似文献
20.
We study conformal biderivations of a Lie conformal algebra. First, we give the definition of a conformal biderivation. Next, we determine the conformal biderivations of loop W(a, b) Lie conformal algebra, loop Virasoro Lie conformal algebra, and Virasoro Lie conformal algebra. Especially, all conformal biderivations on Virasoro Lie conformal algebra are inner conformal biderivations. 相似文献